The applet is an animation of the interacting particle system called TASEP in continuous. The particles, the small blue dots on the bottom line of the animation, try to jump on their neighbor site with rate one, except the first one with rate alpha. This can happen only when the site is empty.
Important types of initial conditions are the step initial condition, where particles occupy all the half negative axis, and (half) flat initial condition, where particles initially are (for example) at every second site (half => only on negative axis).

A way to visualize the configuration of particles consists of associating a line as follows. If there is a particle, then one puts a segment (1,-1), otherwise a segment (1,1). This line is the blue line in the Animation.
Interesting results about limit processes of the surface height can be found in our paper Transition between Airy₁ and Airy₂ processes and TASEP fluctuations in Publications. See also my review paper The universal Airy₁ and Airy₂ processes in the Totally Asymmetric Simple Exclusion Process in Publications.

''User guide''
- Choice of initial conditions: "Half Flat IC" = half flat initial conditions; "Step IC" = step initial conditions;
- Choice of the angle of visualisation: "Angle 45" = the line is visualized as explained above; "Angle 0" = the same line is turned now of -45 degrees
- Nb Particles: is the number of particles which are used in the animation
- Jump Rate 1: is the jump probability of the right-most particle; By setting it small, one can created jam situations. Try it!
- Particles Radius: set the sizes of the particles in the visualization
- Speed: this number is in reality invertly proportional to a waiting time during two iterations and not a speed

The source code is also available.